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If xy < 4, is x < 2 ? (1) y > 1 (2) y > x

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If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink] New post 18 Mar 2012, 03:40
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If xy < 4, is x < 2 ?

(1) y > 1
(2) y > x
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Mar 2012, 05:12, edited 1 time in total.
Added the OA
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Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink] New post 18 Mar 2012, 05:25
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If xy < 4, is x < 2 ?

Notice that in order xy<4 to hold true at least one of the multiples must be less than 2 (if both x and y are more than or equal to 2 then xy>2).

(1) y > 1. If for example y=1.5>1 then x can be 1, so less than 2 or 2 so not less than 2. Not sufficient.

(2) y > x. According to above: y>x\geq{2} is not possible since in this case xy>4, so x must be less than 2. Sufficient.

Answer: B.

Hope it's clear.
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Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink] New post 18 Mar 2012, 20:38
Bunuel wrote:
If xy < 4, is x < 2 ?

Notice that in order xy<4 to hold true at least one of the multiples must be less than 2 (if both x and y are more than or equal to 2 then xy>=2).

(1) y > 1. If for example y=1.5>1 then x can be 1, so less than 2 or 2 so not less than 2. Not sufficient.

(2) y > x. According to above: y>x\geq{2} is not possible since in this case xy>2, so x must be less than 2. Sufficient.

Answer: B.

Hope it's clear.


Yes Bunuel. It's clear. Thanks! :)
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Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink] New post 17 Jun 2013, 04:03
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Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink] New post 17 Jun 2013, 23:40
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Smita04 wrote:
If xy < 4, is x < 2 ?

(1) y > 1
(2) y > x


From F.S 1, when y = 4, x = 0.5, xy<4 and x<2.Hence a YES for the question stem. However, for y = 3/2 and x = 2, xy<4 and x=2, hence a NO for the question stem.Insufficient.

From F. S 2, we know that y>x.

Had y been equal to x, we would have x*x<4 --> |x|<2 --> -2<x<2

However, as y>x, to maintain the above given inequality, the value of x will have to reduce even further. Thus, x <2. Sufficient.

B.
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Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink] New post 24 Jul 2013, 11:54
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Bunuel wrote:
If xy < 4, is x < 2 ?

Notice that in order xy<4 to hold true at least one of the multiples must be less than 2 (if both x and y are more than or equal to 2 then xy>2).

(1) y > 1. If for example y=1.5>1 then x can be 1, so less than 2 or 2 so not less than 2. Not sufficient.

(2) y > x. According to above: y>x\geq{2} is not possible since in this case xy>2, so x must be less than 2. Sufficient.

Answer: B.

Hope it's clear.



Hi Bunuel,

I guess the xy>2 should be replaced by xy>4 in above solution
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Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink] New post 24 Jul 2013, 11:57
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up4gmat wrote:
Bunuel wrote:
If xy < 4, is x < 2 ?

Notice that in order xy<4 to hold true at least one of the multiples must be less than 2 (if both x and y are more than or equal to 2 then xy>2).

(1) y > 1. If for example y=1.5>1 then x can be 1, so less than 2 or 2 so not less than 2. Not sufficient.

(2) y > x. According to above: y>x\geq{2} is not possible since in this case xy>2, so x must be less than 2. Sufficient.

Answer: B.

Hope it's clear.



Hi Bunuel,

I guess the xy>2 should be replaced by xy>4 in above solution


Typo edited. Thank you. +1.
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Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink] New post 27 Jul 2013, 01:56
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Have a somewhat different solution for this one.

Given that XY <4 ...... Is X<2???

(1). Y > 1 => Y = GT 1 (Where GT = Greater than)

XY < 4 => X < (4/Y) (We can divide by a number >1 both sides)

=> X < (4/GT1) = > X < LT4 = > X < 4 Not sufficient as X can be 3 , 2 ,1 and so on so forth.

(2). Y>X

=> X GTX < 4

Substituting values X=2 , 2*3 < 4 Not true
X=1 , 1*2 < 4 true

Hence (B) !!
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Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink] New post 27 Jul 2013, 18:08
Smita04 wrote:
If xy < 4, is x < 2 ?

(1) y > 1
(2) y > x


Alternate solution (rather alternate interpretation) for this problem -
xy < 4 or x < 4/y

(1) y > 1: Interpret 4/y as 4/(1 and increasing). This implies x can be <2 or >2 - So not sufficient

(2) y > x: Interpret xy < 4 as x2<4 and since y is greater than x, it implies that x < 2 - So sufficient

Ans.
[Reveal] Spoiler:
B

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Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink] New post 27 Jul 2013, 20:13
- A is insufficient.
- Option B. what if x or y is negative integer. I don't see you mentioned it in your answer.
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Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink] New post 27 Jul 2013, 20:52
nguyenduong wrote:
- A is insufficient.
- Option B. what if x or y is negative integer. I don't see you mentioned it in your answer.


nguyenduong,

Interpretation should be based on given (true) statements. Given here xy<4 and for pt. (2) y>x.

Take any signs, y has to be greater than x or greater part of the multiplication with x resulting in a product smaller than 4.
Consider if xy was 4 (xy=4) and y=x then both x & y would have been + /- 2. Now when the product reduces (product < 4), x has to be always less than the equal contribution i.e. 2.

Hope I could explain.
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Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink] New post 28 Jul 2013, 03:48
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nguyenduong wrote:
- A is insufficient.
- Option B. what if x or y is negative integer. I don't see you mentioned it in your answer.


The question asks whether x<2. Now, for (2) if x is negative, then x<0<2 and if y is negative, then x<y<0<2. In either case we have an YES answer to the question.
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Re: If xy < 4, is x < 2 ? (1) y > 1 (2) y > x [#permalink] New post 06 Aug 2014, 06:50
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